Related papers: Towards a SAT Encoding for Quantum Circuits: A Jou…
Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for…
As fault-tolerant quantum computers scale, certifying the accuracy of computations performed with encoded logical qubits will soon become classically intractable. This creates a critical need for scalable, device-independent certification…
Quantum computing has made tremendous improvements in both software and hardware that have sparked interest in academia and industry to realize quantum computing applications. To this end, several steps are necessary: The underlying problem…
Investigating the classical simulability of quantum circuits provides a promising avenue towards understanding the computational power of quantum systems. Whether a class of quantum circuits can be efficiently simulated with a probabilistic…
A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a…
We define syntax and semantics of quantum circuits, allowing measurement gates and classical channels. We define circuit-based quantum algorithms and prove that, semantically, any such algorithm is equivalent to a single measurement that…
Quantum computers are a revolutionary class of computational platforms with applications in combinatorial and global optimization, machine learning, and other domains involving computationally hard problems. While these machines typically…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
We investigate Clifford+$T$ quantum circuits with a small number of $T$-gates. Using the sparsification lemma, we identify time complexity lower bounds in terms of $T$-gate count below which a strong simulator would improve on the…
Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…
Two main techniques have been used so far to solve the #P-hard problem #SAT. The first one, used in practice, is based on an extension of DPLL for model counting called exhaustive DPLL. The second approach, more theoretical, exploits the…
In breakthrough work, Bravyi, Gosset, and K\"{o}nig (BGK) [Science, 2018] unconditionally proved that constant depth quantum circuits are more powerful than their classical counterparts. Their result is equivalent to saying that a…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
In the foreseeable future, toolchains for quantum computing should offer automatic means of transforming a high level problem formulation down to a hardware executable form. Thereby, it is crucial to find (multiple) transformation paths…
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…
Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable…
In this article we investigate the possibility of encoding classical information onto multipartite quantum states in the distant laboratory framework. We show that for all states generated by Clifford operation there always exist such an…